Notre Dame Journal of Formal Logic

Halldén Completeness for Relevant Modal Logics

Takahiro Seki

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Abstract

Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.

Article information

Source
Notre Dame J. Formal Logic, Volume 56, Number 2 (2015), 333-350.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1429277355

Digital Object Identifier
doi:10.1215/00294527-2864334

Mathematical Reviews number (MathSciNet)
MR3337384

Zentralblatt MATH identifier
1339.03020

Subjects
Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
Halldén completeness relevant modal logics Routley–Meyer semantics van Benthem–Humberstone theorem Sahlqvist formulas

Citation

Seki, Takahiro. Halldén Completeness for Relevant Modal Logics. Notre Dame J. Formal Logic 56 (2015), no. 2, 333--350. doi:10.1215/00294527-2864334. https://projecteuclid.org/euclid.ndjfl/1429277355


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References

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